Irregular shapes

Definition

Irregular shapes are two dimension structure which lies in a plane. These shapes will not have all sides equal and all angles equal. Irregular shape is denoted as when all the sides of the shapes having different length and the value of angles should not be same for all the angles. For better understanding we should know the difference between regular and irregular shapes. Regular shapes have equal angles and equal sides for example regular hexagonal, regular pentagon etc.

Below are some examples of regular and irregular shapes:
Regular Shapes:
Regular Shapes
Above shapes, triangle, square, pentagon and hexagon, having same sides and same angles.

Irregular Shapes:
Irregular Shapes

We can not define above shapes. Each figure have different angles and different side sizes.

Area and Perimeter

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Irregular shapes are combination of regular shapes. There is not a particular formula to find the area and perimeter of these shapes.
Follow below steps to find area and perimeter of irregular shapes:
Step 1: Break irregular shape into regular shapes.

Step 2: Find all of the missing sides of the irregular shape.

Step 3: For perimeter, find the sum of all the sides.

Step 4: For area, calculate the area for each of regular shape and add the results.Let us understand with the help of an example how to find area and perimeter of an irregular shape.
Example: Find the area and perimeter of below figure.
Square Irregular Shapes

Solution: The above figure has two regular shapes, a square and a right triangle.
First find the unknown sides.
Since below part of the figure is a square hence all the sides are equal. Each side is equal to 10.

Square Shapes joint with Triangle

Slant height of shape can be find by using Pythagoras theorem.

i.e. Hypotenuse = 32+42−−−−−−√ = 5

Perimeter of figure = Sum of all sides = 10 + 10 + 14 + 5 + 7 = 46

Area of figure = Area of square + Area of right triangle

= (Side)2 + 12 * Base * Height

= 102 + 12 * 3 * 4

= 100 + 6

= 106
Therefore area of given shape is 106 sq. units.

How to Draw?

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There is not a particular way to draw irregular shapes. To draw an irregular shape just draw some straight lines on the paper and end line at point where started drawing to draw a closed plane shape.

While drawing irregular shapes should not think about the length of sides and measure of angles. Because these shapes having different length and the different value of angles.

Examples

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Example 1: Find the area of shape given below:

Rectangle with SemiCircle

Solution: Given shape is divided into two regular shapes, a semicircle and a rectangle.
To find area of given shape first find area of semicircle and area of rectangle. Then add both the results.

Rectangle with SemiCircle with Dimension
Area of semicircle:
Radius = diameter2 = 82 = 4

Area = 12 π Radius2

= 12 × 227 × 42

= 1767

Area of rectangle:

Area = length × width

= 17 × 8

= 136
Now total area of irregular shape = Area of semicircle + Area of rectangle

= 1767 + 136

= 11287
= 161.14

Area of given shape is 161.14 sq. units

Example 2:  Find the area and perimeter of the figure below.

Two Regular shapes
Solution: The above figure is divided into two regular shapes, a square and a rectangle.

First find the unknown sides. Since below part of the figure is a rectangle hence its opposite sides are equal.
Two Regular shapes with joint
Area =  Area of rectangle + Area of square

= (length * breadth) + side2

= (8 * 4) + 52

= 32 + 25

= 57

Perimeter = Perimeter of rectangle + Perimeter of square

= 2(length + breadth) + 4 Side

= 2 (8 + 4) + 4 * 5

= 24 + 20

= 44

Example 3: Find the area figure ABCD.
Irregular Shapes Examples
Solution: Area of ABCD = Area of CED + Area of ABCE

= 12 × 20 × 5 + 10 × 20

= 50 + 200

= 250

Therefore area of given shape is 250 sq. units.

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